Deflection method previously we have discussed forceflexibility methods of analysis of statically indeterminate structures. Application of slopedeflection equations to statically indeterminate beamsindeterminate beams. Macaulays method is a means to find the equation that describes the deflected shape of a beam. When a point of zero slope is known, either from symmetry or from supports, a tangent drawn at this point will frequently be useful. A numerical example has been solved by using the basic slope deflection equation and then solved again by using the presented new modified equation.
Frames with sidesway civil engineering ce notes edurev is made by best teachers of civil engineering ce. The slope deflection method is still used in quick analysis, preliminary design, checking the analysis, and for. The change in slope of the deflected shape elastic curve of a beam between two points a and b is equal to the area under the mei diagram between these points. Application of slope deflection equations to statically indeterminate beamsindeterminate beams. Degrees of freedom are treated as unknowns in slopedeflection method. Using the slopedeflection method, determine the member end moments in the indeterminate beam shown in figure 12. Civil engineering solved examples for slope and deflection. A numerical example has been solved by using the basic slopedeflection equation and then solved again by using the presented new modified equation. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. The slope and deflection of the right end of the beam due to v 2 two equations. Wood page 19 of 26 additional slopedeflection insights.
This tutorial goes through a slope deflection method example problem that is 4 degrees statically indeterminate and 1 degree kinematically indeterminate. Before macaulays paper of 1919, the equation for the deflection of beams could not be found in closed form. Introduction slopedeflection method is the second of the two classical methods presented in this course. These double integration method tutorials also show up in the mechanics of materials playlist in the beam deflection section. Assume a and c are pinned and b and d are fixed connected.
An important characteristic of the slope deflection method is that it does not become increasingly complicated to apply as the number of unknowns in the problem increases. If the frame is statically indeterminate to degree one, then one of the support reactions must be selected as the redundant. We will eliminate the rotation of the simple support at end e by. Slope deflection method a h m 531 structures 2 slope. Indeterminate structure a statically indeterminate system means that the reactions and internal forces cannot be analyzed by the application of the equations of static alone.
Slope at the ends of a simply supported beam with center point. The slopedeflection method uses displacements as unknowns and is referred to as a displacement method. Ei 1 m from calculus, the curvature of the plane curve shown is given by. Slope deflection method examples purdue engineering. Using momentdisplacement relations, moments are then known.
Chapter three includes an introduction to the slope deflection method, degrees of freedom, derivation of the slope deflection equation, equilibrium conditions for joint and shear, and solved. The slopedeflection method for beams will be illustrated using the example structure shown in figure 9. The structure is thus reduced to a determinate structure. Nodes a and c are fixed and so do not have any degreesoffreedom dofs. The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by george a. Identify all kinematic degrees of freedom for the given problem. This tutorial goes through another slope deflection method example problem that is 2 degrees statically indeterminate and 2 degrees kinematically indeterminate. In force method,theunknown redundant forces are determined first by solving the structures compatibility equations. That is, node displacements are treated as the unknowns, after solving the stiffness equation for displacements, member forces and reactions are obtained. What is the difference between slope deflection method and. All the steps of these examples are very well explained and it is expected that after going through these solved examples the students will improve their problem solving skills. This document is highly rated by civil engineering ce students and has been viewed 372 times.
Use slope deflection equations to find the resultant end moments for the continuous beam shown in figure 74a. Degrees of freedom are treated as unknowns in slope deflection method. A beam abc, 10m long, fixed at ends a and b is continuous over joint b and is loaded as shown in fig. An important characteristic of the slopedeflection method is that it does not become increasingly. Basic idea of slope deflection method the basic idea of the slope deflection method is to write the equilibrium equations for each node in terms of the deflections and rotations.
Deflection method in displacement method,theunknown displacements are determined first by solving the structures equilibrium equations. The author shall not be liable to any viewer of this site or any third party for any damages arising from the use of this site, whether direct or indirect. By solving these equations, the unknown rotations are found out. Method aims determine the slope and deflection by using moment area method expected outcomes. Force method for frames one redundant force indeterminate frames can be solved in the same manner as indeterminate beams. Introduction to beam deflection and the elastic curve equation.
Objective to obtain slope and deflection of beam and frame structures using slopedeflection method 3 4. Example 1 determine the moments at b and d, then draw the moment diagram. Slopedeflection method the slopedeflection method uses displacements as unknowns and is referred to as a displacement method. A couple of examples are solved to illustrate the slopedeflection equations. The procedure is the same whether it is applied to beams or frames. Determine the slope and deflection at the end a of. The slope deflection method was widely used for more than a decade until the moment distribution method was developed. Find deflection of a simply supported beam with distributed load. Find deflection and slope of a cantilever beam with a point load. Slope deflection method beam structure deformation. Determine the slope and deflection at the free end of the cantilever beampoint b. Analysis of statically indeterminate structures by the. We have provided illustrated solved examples on calculation of slope and deflection of cantilever, simply supported beams and frames by diffferent methods like double integration, macaulays method and unit load method.
Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. The center column keeps ridge point c from displacing vertically. Note that in the solution, for spans ab and cd the shorthand slope deflection formula along with pinnedfixed fems are used. An important characteristic of the slopedeflection method is. This document is highly rated by civil engineering ce students and has been viewed 1480 times.
The slope and deflection of the right end of the beam due to m 2 two equations. In the slopedeflection method, the moments at the ends of the members are expressed in terms of displacements and end rotations of these ends. These rotations must be considered when writing the slopedeflection equations for the columns, as will be demonstrated in the solved examples. An introduction part 1 civil engineering ce notes edurev is made by best teachers of civil engineering ce. By application of the second areamoment theorem, determine the tangential deviation at the point where the beam deflection is desired and at any other points required. A numerical example has been solved by using the basic slopedeflection. In the slope deflection method the individual equations are relatively easy to construct regardless of the number of unknowns. Pdf new modification for slope deflection equation in. It is given that the modulus of elasticity, e, is 29,000 ksi and the moment of inertia, i, is 400 in4. Solve the problem using both doubleintegration method and momentarea theorems.
Able to analyze determinate beam deflection and slope by moment area method. Solve example 8 assuming the supports at a and e are fixed. Degrees of freedom joints c, d and e are free to rotate. In the book, the theory and practice of modern framed structures, written by j. The slopedeflection method is a structural system analysis method developed by heinrich manderla and otto mohr which was later presented by professor g.
Pdf the slopedeflection method is one of the classical displacement. Determine the slope and deflection at the end a of the cantilevered beam. Deflections by superposition iowa state university. Slope deflection method and moment distribution method are both stiffness methods. Now, the required equation to solve for the rotation. From this equation, any deflection of interest can be found. Maney this method was later replaced by moment distribution method which is more advanced and useful students are encouraged to study. Introduction structural analysis method for beams and frames introduced in 1914 by george a.
Solving continuous beam by slopedeflection equations. The given beam in figure 74a is statically indeterminate of degree 1. Pdf new modification for slope deflection equation in structural. Equilibrium equations end moments are expressed in terms of unknown rotation.